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Vacuum tube theory
Edison Effect
Thermionic emission
Thermionic emission is the emission of electrons from the surface of a heated cathode or
filament.
Type of Cathodes: directly heated, indirectly heated
Many Directly heated triodes (DHT) have been the sought-after tubes for audiophiles.
Popular power DHTs are 10, 10Y, 45, 50, 71, 2A3, 6A3, 6B4G, 300B, 211, 805, 845.
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Cathode materials
Material
Working
temp., ℃
features
Tungsten
2200-2500
1. High temperature
2. Long life
3. High emission, high power
Thoriated
tungsten
1900
1. Thorium is a low radiative material. It emits mainly
alpha particles.
2. Lower working temperature
3. Long life
4. High emission, high power (211, 805, 845).
Oxide coated
800-1150
1. The most common coatings are of strontium and
barium oxides.
2. Low working temperature.
3. Used for receiving tubes.
The diode
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Space Charge: Electrons are emitted to form the cloud of electrons around the cathode,
with each electron containing one negative charge, makes this area highly negative and
thus gives it the name “space charge”. For any given cathode material at a certain given
temperature, only so many electrons can be contained in the electron cloud. Other
electrons will be prevented from entering the cloud from the cathode unless electrons in
the cloud leave, as some do when the plate is made positive.
Plate dissipation
Diode circuit
1. Half Wave
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2. Full Wave
Indirectly heated full wave rectification
Directly heated full wave rectification
The Triode
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(a) Basic indirectly heated triode circuit
(b) Basic directly heated triode circuit
Typical grid structures
The grid controls the amount of current flowing from cathode to plate. As the grid is
more negative, the electrostatic force from the grid to repel the amount of current flowing
from cathode to plate is larger. Thus the more negative the grid, the less the current flows
from cathode to plate.
The triode tube is often called a valve, which is descriptive of the way that the grid
controls the currents the current flow from cathode to plate.
Positive Grid Voltage
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With the grid positive, some of the electrons will flow in the grid circuit to the grid
battery. This current is called grid current.
In most applications the grid new goes positive. There are some cases, however, when
the grid is made positive for a short period of time in each cycle. Some examples are in
the horizontal amplifier in television sets and in radio transmitters and oscillators.
Static Grid-Voltage Curves (Plate Characteristics)
Plate current VS plate voltage for E88CC
Amplification Factor, μ (mu)

Va
Vg
Where
Va is the change of anode voltage
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V g is the change of grid voltage
When calculating from the equation, we will obtain a negative mu. This means there is
a phase inverse between the grid voltage change and the anode voltage change.
Calculation of Amplification Factor
6DJ8: 33
12AU7:
Anode Resistance: ra (or Plate Resistance, rp)
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Plate resistance is slightly different from point to point.
ra 
It can be calculated by:
V a
I a
Where
I a is the change of anode current
Mutual Conductance (or transconductance): gm
The mutual conductance gm of a valve is the ratio of the change in anode current I a to
the change in grid voltage V g , with anode voltage held constant.
gm 
I a
Vg
The unit of gm is 1/Ohm (A/V), which is called mho.
be too big, it is common to use μmho.
Instead of using mho, which may
1 μmho = 10-6 mho1
Relationship between ra, gm and μ.
gm 
I a
I Va Va I a
1 
 a

 
Vg Vg Va Vg Va
ra ra
Ex. Using the following 6DJ8 Plate Characteristics diagram to find its mu, gm, ra.
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6DJ8 Plate Characteristics diagram
Grounded Cathode Amplifier
1. Easily biased.
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2. Small part count.
3. Miller Effect capacitance.
4. Gain never exceeds the mu of the tube in use.
5. The plate resistor can be replaced with a constant current source, either tube or
solid-state.
6. The maximum voltage occurs when (roughly): Rk = (ra + Rp) / μ.
7. If the cathode resistor is bypassed, both the gain and the distortion will increase, while
the output impedance will decrease.
8. The cathode resistor could be replaced with a diode or LED or a precision voltage
reference IC or even a rechargeable ni-cad battery.
1. Grid Bias (Fixed Bias)
Load Line
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Plate characteristics for 12AX7 (ECC83)
Find mu and ra
voltage gain of the fixed bias amplifier
Av  
Rp
R p  ra
2. Self Bias (Cathode Bias)
(2.1) Cathode decoupling (or bypass) capacitor
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Capacitor Cin is the input coupling capacitor. It is used to isolate the grid circuit from the
DC voltage at the output of the previous circuit.
Rg is the grid resistor, which is used to provide a reference voltage for the grid circuit
(ground in this case). It is usually a high value but normally should not exceed 1 M
Ω. This resistor controls the input impedance of the stage.
Rk is the cathode resistor, which is used to develop the cathode bias voltage.
Capacitor Ck is used to bypass the cathode resistance to ground for AC signals, which
results in a higher gain. Without Ck, there is negative feedback, or degeneration, which
reduces the gain of the stage and increases the output impedance.
Resistor Rp is the plate load resistor. The output signal voltage is developed across this
resistor, by the action of the plate current flowing through it.
Capacitor Cout is the output coupling capacitor. It is used to isolate the plate DC voltage
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from the next stage it is driving.
Input Impedance
Z in  R g
Output Impedance
Z out  R p // ra 
R p ra
R p  ra
voltage gain
Av  
Rp
R p  ra
Frequency response due to input circuit:
The low frequency response due to the input circuit is controlled by Cin and Rg. These
components act as a high-pass filter with a -6dB/octave (-20dB/decade) slope and a lower
-3dB point that can be calculated as follows:
f 
1
2Cin Rg
The high frequency response due to the input circuit is controlled by the output
resistance of the stage driving the common-cathode stage and the input capacitance of
the stage. The input capacitance is governed primarily by the Miller capacitance of the
stage, and can be calculated as follows:
Cin =Cgk + Cgp*(Av + 1)
where:
Cgk = the grid-to-cathode capacitance
Cgp = the grid-to-plate capacitance
Av = the stage voltage gain
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Frequency response due to output circuit
The low frequency response due to the output circuit is controlled by Cout, and the output
impedance of the stage. If the input impedance of the next stage is very high, then the
low -3dB point that can be calculated as follows:
f 
2 ( Rout
1
 Z out )Cout
If the output impedance is low when comparing to Rout, the above equation can be
approximated as follows:
f 
1
2RoutCout
Frequency response due to the cathode decoupling capacitor
f 
1
2RC k
Where R is the resistance that the cathode capacitor sees.
R  rk // Rk 
rk 
rk Rk
rk  Rk
R p  ra
 1
(2.2) unbypassed cathode bias
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Input Impedance
Z in  R g
Output Impedance
The internal plate resistance will increase if there is negative feedback due to an
unbypassed cathode resistor, and the voltage gain of the stage will decrease as well.
ra'(unbypassed Rk) = ra + (μ + 1)*Rk
Z out  R p // ra ' 
R p ra '
R p  ra '
Voltage Gain
Av  
Rp
R p  ra '
Frequency response due to input circuit:
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f 
1
2Cin Rg
Frequency response due to output circuit
f 
2 ( Rout
1
 Z out )Cout
If the output impedance is low when comparing to Rout, the above equation can be
approximated as follows:
f 
1
2RoutCout
Miller capacitance
CMiller = (A+1) Cag
Where Cag is the grid to plate interelectrode capacitance.
Maximum Rating
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1. Maximum plate dissipation
Normally the maximum plate dissipation is not a problem for line amplifier or voltage
amplifier. However it should be taken care of in the power output stage since we always
want to get the maximum output from a tube.
2. Maximum plate voltage
This is the voltage between the cathode and the plate.
3. Maximum Grid Resistance, Rg
The input grid resistor should not normally exceed 1 megaohm with indirectly-heated
valves. The output grid resistor may be the maximum recommended for the following
stage by the valve manufacturers – usually 0.5 megaohm for power valves with cathode
bias.
Ex. 2A3 directly heated triode
EX. 6DJ8
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4. Peak heater-cathode voltage
Ex. 6DJ8
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The Tetrode
Screen grid
Secondary Emission
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The Pentode
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Screen Grid and Suppressor or Suppress Grid
Using the EF86 small-signal pentode
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gm = mu/ra = 5000/2500000 = 0.002 mho = 20,000 micromho
Gain = gm x Rp
= 20,000 x 10-6 x 47 x 103
= 94
The Beam Power Tetrode
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6L6
Cathode Follower (CF)
The cathode follower has a voltage gain of slightly less than 1, a low output resistance,
typically less than 1 kΩ, a high input resistance, and is non-inverting. The cathode
follower is an excellent buffer stage for driving a tone stack, effects loop, power valve or
any circuit which would otherwise present a heavy load to a "normal" stage. The cathode
follower also produces a unique quality compression when DC coupled, which is to be
found in most of the classic amp designs.
1. Fixed bias cathode follower
The cathode follower is simply a special case of the common cathode amplifier with
100% negative feedback.
Av 
A0
A0



1  A0 1  A0 1  
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A0 is the gain of the original grounded cathode amplifier.
output resistance
Z out  rk // Rk
Where
rk 
ra
1

  1 gm
2. Cathode bias cathode follower
For cathode bias cathode follower and DC direct-coupling cathode follower, their heater
voltage may need to be elevated.
Design Example
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76 and 6SN7 cathode follower line stage
The Shunt Regulated Push-Pull (SRPP) amplifier
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Av 
1 ( 2 Rk  ra 2 )
ra1  ra 2  Rk ( 2  1)
output resistance
Z out 
ra 2 ( Rk  ra1 )
ra1  ra 2  Rk ( 2  1)
Grounded Grid Amplifier
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